As the size of distributed systems keeps growing, the peer to peer communication paradigm has been identified as the key to scalability. Peer to peer overlay networks are characterized by their self-organizing capabilities, resilience to failure and fully decentralized control. In a peer to peer overlay, no entity has a global knowledge of the system. As much as this property is essential to ensure the scalability, monitoring the system under such circumstances is a complex task. Yet, estimating the size of the system is a core functionality for many distributed applications to parameter setting or monitoring purposes. In this paper, we propose a comparative study between three algorithms that estimate in a fully decentralized way the size of a peer to peer overlay. Candidate approaches are generally applicable irrespective of the underlying structure of the peer to peer overlay. The paper reports the head to head comparison of estimation system size algorithms. The simulations have been conducted using the same simulation framework and inputs and highlight the differences in cost and accuracy of the estimation between the algorithms both in static and dynamic settings.
